Question

4. A call option currently sells for $7.75. It has a strike price of $85 and seven months to maturity. A put with the same strike and expiration date sells for $6.00. If the risk-free interest rate is 3.2 percent, what is the current stock price?

5. Suppose you buy one SPX call option contract with a strike of 1300. At maturity, the S&P 500 Index is at 1321. What is your net gain or loss if the premium you paid was $14?

6.What is the value of a call option if the underlying stock price is $78, the strike price is $80, the underlying stock volatility is 42 percent, and the risk-free rate is 5.5 percent? Assume the option has 110 days to expiration.

7.You are managing a pension fund with a value of $480 million and a beta of 0.90. You are concerned about a market decline and wish to hedge the portfolio. You have decided to use SPX calls. How many contracts do you need if the delta of the call option is 0.64 and the S&P Index is currently at 1250?

Answer 1

(4) Call Premium = C = $ 7.75, Strike Price = S = $ 85, Time to Maturity = 7 months, Put Premium = P = $ 6 and let the current stock price be $ S, Risk-Free Rate = Rf = 3.2%

Now, two call options with the same underlying, same expiry and equal strike price follow put-call parity relationship which is stated as shown below:

C + PV of Strike Price = S + P

7.75 + 85 / e^[(7/12) x 0.032] = S + 6

S = 7.75 + 83.42805 - 6 = $ 85.17805 ~ $ 85.18

NOTE: Please raise separate queries for solutions to the remaining unrelated questions, as one query is restricted to the solution of only one complete question with up to four sub-parts.